Abstract

Let R be a communicative noetherian ring with identity, and let E be a finite generated module of projective dimension 2 and second Betti number 3. We establish sufficient conditions for the integrity of the symmetric algebra of E in relation to the aciclicity of the Z (E) - complex of approssimation of E and to the depth of the esternal power of either the sizigy of E or theirs duals and biduals.